The present invention relates to tuning filters.
Filters are used extensively in the field of electronics and are routinely constructed on integrated circuits (ICs). They are typically constructed using combinations of resistors, capacitors, and amplifiers (RC filters or Gm-C filter) and are designed to remove unwanted components (such as noise) from signals by passing one band (the pass band) of frequency and rejecting another (the stop band). For example, filters may be low pass filters (LPFs), which pass input signals with low frequencies, or high pass filters (HPFs), which pass input signals with high frequencies. The corner frequency of a filter (fc) represents the frequency boundary at which the filter will pass/block components of an input signal. Moreover, the transfer function of a filter, which is a function of its corner frequency, determines an output of the filter in response to a given input.
FIG. 1(a) is an example of an active RC filter 100 with an input voltage Vin an output voltage Vout. The filter 100 includes input resistors R101, an amplifier 102, feedback resistors R103, and feedback capacitors C104. Resistors R101, R103 and capacitors C104 are programmable components, therefore their values can be increased or decreased based on requirements of a system implementing the filter 100. The transfer function of the filter 100 is given by the following equation:
                                          V            ⁢            out                                V            ⁢            in                          =                                            R              103                                      R              101                                ⁢                      1                          1              +                              j                ⁢                                  f                                      f                    c                                                                                                          Eq        .                  (          1          )                    where
      R    103        R    101  is the DC gain of the filter,
      f    c    =      1          2      ⁢                          ⁢      π      ⁢                          ⁢              R        103            ⁢              C        104            is the corner frequency of the filter, and R103C104 is the time constant, τ, of the filter 100.
FIG. 1(b) is an example of an active RC filter 110 with a current input (called a “trans-impedance amplifier” or a TIA). The filter includes an amplifier 112, programmable feedback resistors R111, and programmable feedback capacitors C113. The transfer function of the filter is given by the following equation:
                                          V            ⁢            out                                I            ⁢            in                          =                              -                          R              111                                ⁢                      1                          1              +                              j                ⁢                                  f                                      f                    c                                                                                                          Eq        .                  (          2          )                    where
      f    c    =      1          2      ⁢                          ⁢      π      ⁢                          ⁢              R        111            ⁢              C        113            is the corner frequency of the filter 110.
FIG. 1(c) is an example of transconductance-capacitance filter 120 (called a “Gm-C” filter). The filter 120 includes an amplifier 122 with programmable transconductance (Gm) and a programmable capacitor C123. The transfer function of the filter 120 is given by the following equation:
                                          V            ⁢            out                                V            ⁢            in                          =                  1                      1            +                          j              ⁢                              f                                  f                  c                                                                                        Eq        .                                  ⁢                  (          3          )                    where
      f    c    =      Gm          2      ⁢                          ⁢      π      ⁢                          ⁢              C        123            is the corner frequency of the filter 120.
Under ideal circumstances, the filters 100, 110, and 120 in FIGS. 1(a)-(c), respectively, would operate at their designed corner frequencies fc. In reality, however, variations in manufacturing processes and operating conditions of ICs, such as voltage and temperature, result in deviations in the actual value of filter components when compared to their design values. For example, in active RC filters resistors and capacitors could vary as large as ±15% across wafers. Amplifier transfer functions also vary significantly over process, voltage, and temperature. These variances significantly impact the transfer function (and corner frequency) of a filter. Therefore, in order to obtain a required transfer function for an on-chip RC filter, the filter must be tuned. A filter can be tuned by varying its components (resistors and capacitors, for example) until a desired output is realized. For example, in FIGS. 1(a) and (b) above, fc can be coarsely turned by varying the resistor values and finely tuned by varying the capacitor values. In FIG. 1(c), fc can be tuned by varying either the transconductance of the amplifier Gm or the capacitor value.
Conventional filter tuning methods focus on tuning replica components and/or filter circuits on the IC and using the tuning results to modify the components on the actual filter that needs to be tuned. One conventional method includes creating a replica filter circuit on the IC, tuning the replica circuit to a desired corner frequency, and applying the tuning results to the actual filter in need of tuning. Tuning replica filter circuits, however, has several disadvantages. Most importantly, because of inconsistencies between the replica filters and the actual filters, using tuning results derived from replica circuits to tune actual filters may result in tuning inaccuracies. Additionally, these tuning circuits take up additional space on the ICs, which is undesirable.
Another conventional tuning method includes placing replica components (such as the resistors or capacitors of an RC filter) on the IC, applying current to the replica components, and varying the components until a desired output is realized. However, this method has the same disadvantages of the previously mention tuning method due to replica component variations. Additionally, this method fails to account for amplifier transfer function variances, which also significantly impact the corner frequency of a given filter.
Moreover, neither of the conventional methods account for filter response delays caused by the finite bandwidth of filter components. Filter response delays significantly impact tuning accuracy, especially in high bandwidth applications.
Thus, the inventors recognized a need in the art for an improved filter tuning circuit and method that improves tuning accuracy while reducing the cost of the system.